Question $4$

$[25/100$ marks$]$

Describe the Gravity Model method for trip distribution. $[10/25]$

To illustrate the application of the gravity model, consider a study area consisting of three zones. The number of productions and attractions, and the average travel times between each zone are shown in Tables $4\mathrm{.}1$ and $4\mathrm{.}2,$ respectively. Assume $K_i,$ the socioeconomic adjustment factor, is the same unit value for all zones. The friction factor $F$ values have been calibrated and shown in Table $4\mathrm{.}3$ for each travel time increment. Determine the number of zone$-$to$-$zone trips through two iterations. $[15/25]$

Table $4\mathrm{.}1$ Trip Production and Attractions for a Three$-$Zone Area

$\backslash$table$[[$Zone$,1,2,3,$Total$],[$Trip production,$140,330,280,750],[$Trip attraction,$300,270,180,750]]$

Table $4\mathrm{.}2$ Travel Time between Zones $($min$)$

$\backslash$table$[[$Zone$,1,2,3],[1,5,2,3],[2,2,6,6],[3,3,6,5]]$

Table $4\mathrm{.}3$ Travel Time versus Friction Factor

$\backslash$table$[[$Time $(min),F$